Some observations about the application of Fick's first law for membrane separation of multicomponent mixtures

Abstract

According to Fick's first law of diffusion, permeation flux of a permeant through a pore-free dense polymeric membrane with respect to a fixed frame of reference is equal to the sum of the bulk and diffusional flux. Under ideal conditions and low downstream (permeate) pressure, membrane permeability, P A , of component A is equal to the product of the mobility coefficient, D A , and the solubility coefficient, S A . The definition of membrane permeability as stated above can be derived using Fick's first law of diffusion when the frame of reference (bulk flux) term is negligible. When analyzing the transport of permeant through pore-free dense polymeric membrane, the bulk flux contribution is usually assumed to be negligible when the sorption levels of the components are small. However, this assumption can be erroneous in the case of multicomponent mixtures when the permeation flux of one of the permeant is much higher than the others. Two examples will be discussed to demonstrate that neglecting the bulk flux contribution might lead researchers to incorrect conclusions on the material science aspects of the membrane separation. The first example is CO 2 CH 4 gas separation using a dense pore-free glassy polymeric membrane and the second example is the removal of traces of phenol from water using a polyether-block-polyamide polymer.